The investigation of melting curve Tm(ρ) under high pressures has practical applications both for temperature induced softening of yield strength of materials and for the reasonable partitioning of hot contributions from that of cold part. In this paper, we make use of the experimental results of shock melting of Al, Cu, Pb and take account of the transition of Gruneisen coefficients γ(ρ) from solid-state value to liquid-state value, and thus provide the scaling of melting curve Tm(ρ) through Lindemann melting law. Since Lindemann law is closely related with the Gruneisen coefficient γ(ρ), the scaling of Tm(ρ) by the experiment data of the shock melting temperature is equivalent to the scaling of γ(ρ) by experiment.